Timeline for Axiomatizing Gross-Zagier formulae
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2012 at 12:02 | comment | added | Victor Rotger | Ok, I just managed. | |
| Oct 24, 2012 at 11:08 | comment | added | Victor Rotger | But it's not displaying well, I don't understand what I'm typing wrong. | |
| Oct 23, 2012 at 13:20 | comment | added | Victor Rotger | I just edited the question in order to focus it on the aspects I would like to learn more about. | |
| Oct 9, 2012 at 11:20 | history | edited | Olivier | CC BY-SA 3.0 |
Typo corrected
|
| Oct 9, 2012 at 9:15 | comment | added | David Loeffler | ... When the L-value vanishes "coincidentally", it is probably going to be much more difficult to prove a formula for the derivative in terms of heights etc; it would probably more closely resemble the case of elliptic curves of rank $\ge 2$, where we certainly expect BSD to hold but nobody knows an explicit construction for the necessary points. | |
| Oct 9, 2012 at 9:13 | comment | added | David Loeffler | Just to expand on one of Olivier's remarks: the cases where one can prove a formula for the derivative of an L-function are more or less restricted to ones where the L-function vanishes for "obvious reasons" (e.g. sign-induced vanishing at central critical values for self-dual motives with sign -1; or the trivial zeros of Rankin-Selberg L-functions at s=1 and of modular form L-functions at s=0, corresponding respectively to the Beilinson-Flach and Beilinson-Kato elements). This "obvious" vanishing will, as Olivier remarks, be robust enough to happen generically in a p-adic family. | |
| Oct 9, 2012 at 9:01 | history | edited | Olivier | CC BY-SA 3.0 |
Took into account comments and expanded the answer
|
| Oct 8, 2012 at 21:05 | comment | added | Victor Rotger | Thanks, Olivier, this is the kind of ideas I was looking forward to discuss. The reasons you pose make me agree with you that "it is not straight-forward" to extend the current circle of ideas to non self-dual settings. And I agree even more with you in that it would be fun to learn whether some other ideas can be exploited to push these GZ formulae to some non self-dual scenario. On the geometric side of the formula, notice that I don't require the point to be a Heegner point. And I am an optimist as for whether some sort of GZ formula should hold (not that it'd be easy to prove!). | |
| Oct 8, 2012 at 20:42 | history | answered | Olivier | CC BY-SA 3.0 |